Ubiquitous threshold for coherent structures in solar wind turbulence

(Solar Orbiter Nugget #63 by A. Bendt¹ and S. C. Chapman¹)

1. Introduction

As the solar wind expands, it is heated by a mechanism that is yet to be determined. Turbulence is the chaotic flow of the solar wind plasma, which transports energy from large scales to small, kinetic scales. Turbulence is one possible heating mechanism [1]. Coherent structures, which have temporal coherence in the turbulent flow and are spatially localized, as for example current sheets, and magnetic reconnection events, are one possible mediating mechanism of the turbulent cascade and may also dissipate energy (e.g. [2]). We use Solar Orbiter observations from the MAG and SWA instruments at various distances from the Sun, ranging from 0.3 to 1 au, to determine a threshold beyond which magnetic field fluctuations may be coherent structures.

2. Method 

The Partial Variance Increment (PVI) is routinely used to identify and quantify coherent structures [3]. The threshold of the PVI above which fluctuations may be coherent structures is traditionally identified by comparison to a Gaussian distribution. We use two different wavelet decompositions using the Haar and 10th-order Daubechies (Db10) wavelets which are sensitive to sharp changes and oscillations in the time series respectively. Comparisons of the fluctuation distributions obtained from the Haar and Db10 wavelet decompositions, reveal a core and tail. The tail of the fluctuation distribution is dominated by coherent structures [4]. The transition from core to tail identifies the PVI threshold.

3. Results

Figure 1. Compensated QQ plots discriminate where the Haar (sharp changes) and Db10 (wave-packet) decomposed PVI fluctuation distributions diverge (gray shading) for all solar wind intervals in the kinetic range. The upper panels [(a)–(c)] illustrate the compensated QQ plots (see text). [(d)–(j)] are compensated QQ plots in the kinetic range overplotted for all intervals. These are divided into three categories based on heliocentric distance, (i) 0.3 ⩽ R < 0.4 au, (ii) 0.4 < R < 0.8 au, and (iii) R > 0.8 au (rows), shown for all magnetic field components (columns). The different scales τ are color coded from dark blue (0.25 s) to light blue (2 s). The overplotted PVI threshold of 2.2 (marked by a black vertical line) is the same for all panels, capturing where the Haar and Db10 derived PVI distributions diverge. The gray shaded region determined from the variance of the threshold ranges from 2.1 to 2.7. This threshold is independent of the scale τ of the turbulence and heliocentric distance. Dashed horizontal lines are at PVI ±0.2 for reference.

This threshold coincides with the PVI value where the PVI distributions obtained from the Haar and Db10 wavelets start to depart from each other (see Fig.1). We find a single value for the threshold in each the kinetic and inertial ranges (see Fig.1 & 2). This threshold is independent of heliocentric distance and solar wind conditions. The detailed behaviour of the fluctuations above the threshold varies, reflecting different ways that turbulence develops with distance from the sun (see Fig.1 panels j)-l) and Fig.2 panels g)-i)).

Figure 2. Compensated QQ plots discriminate where the Haar (sharp changes) and Db10 (wavelike) decomposed PVI fluctuation distributions diverge (gray shading) for all solar wind intervals in the inertial range. Compensated QQ plots in the inertial range for all intervals divided into three categories based on heliocentric distance, (i) 0.3 ⩽ R < 0.4 au, (ii) 0.4 < R < 0.8 au, and (iii) R > 0.8 au (rows) shown for all magnetic field components (columns). The different scales τ are color coded from light red (4 s) to dark red (128 s). The overplotted PVI threshold of 2.5 (marked by a black vertical line) is the same for all panels, capturing where the Haar and Db10 derived PVI distributions diverge. The gray shaded region determined from the variance of the threshold ranges from 1.7 and 3.3. This threshold is independent of the scale τ of the turbulence and heliocentric distance. Dashed horizontal lines are at PVI ±0.2 for reference.

4. Conclusions

We find a ubiquitous threshold above which fluctuations may be coherent structures regardless of solar wind conditions in each the kinetic and inertial ranges. This suggests an underlying mechanism governing these coherent structures that is the same regardless of the specific plasma conditions. These results give insight into the evolution of turbulence and possible constraints on the mediating mechanisms of the turbulent cascade.

For further reading, see the related publication: Bendt&Chapman, Phys. Rev. Research, 7, 023176 (2025), https://doi.org/10.1103/PhysRevResearch.7.023176

Affiliations
(1) Centre for Fusion, Space and Astrophysics, Physics Department, University of Warwick, Warwick CV4 7AL, United Kingdom

References
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[2] P. Wu, S. Perri, K. Osman, M. Wan, W. H. Matthaeus, M. A. Shay, M. L. Goldstein, H. Karimabadi, and S. Chapman, Intermittent heating in solar wind and kinetic simulations, Astrophys. J. 763, L30 (2013) https://doi.org/10.1088/2041-8205/763/2/L30
[3] A. Greco, P. Chuychai, W. H. Matthaeus, S. Servidio, and P. Dmitruk, Intermittent MHD structures and classical discontinuities Geophys. Res. Lett. 35, 2008GL035454 (2008) https://doi.org/10.1029/2008GL035454
[4] A. Bendt, S. Chapman, and T. D. de Wit, The relative prevalence of wave packets and coherent structures in the inertial and kinetic ranges of turbulence as seen by Solar Orbiter, Astrophys. J. 971, 179 (2024) https://doi.org/10.3847/1538-4357/ad54bc